The problem of rational theory-choice is the problem of whether choice of theory by a scientist may be objectively rational in the absence of an invariant scientific method. In this paper I offer a solution to the problem, but the solution I propose may come as something of a surprise. For I wish to argue that the work of the very authors who have put the rationality of such choice in question, Thomas Kuhn and Paul Feyerabend, contains all that is needed to solve the problem.